Enhancement of sensors for airborne operation

ABSTRACT

Gravity gradiometers (or gravity gradient instrument, GGI) measure one or more components of the gradient of gravity which is expressed as the gradient of a gravity vector. One or more feedback loops extend from the instrument output to one or more of the accelerometers ( 1–4 ) to compensate for errors. The feedback loops include one or more inputs in addition to the instrument output. The additional inputs include signals representing one or more of: components of attitude, velocity and acceleration, the physical environment and flight conditions, taken alone or in combination.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority under 35 USC §119(a)–(d) of International Application No. PCT/AU03/00297, with aninternational filing date of 12 Mar. 2003, which claims priority toAustralian Application No. PS 1147, filed 18 Mar. 2002, which areincorporated herein by reference in their entirety.

TECHNICAL FIELD

This invention concerns improvements in the performance of a mobilegravity gradient instrument (GGI). Gravity gradiometers measure one ormore components of the gradient of gravity which is expressed as thegradient of a gravity vector, or in other words a tensor, which may bewritten as follows:

${\begin{matrix}g_{xx} & g_{yx} & g_{zx} \\g_{xy} & g_{yy} & g_{zy} \\g_{xz} & g_{yz} & g_{zz}\end{matrix}}\begin{matrix}{{units}\mspace{14mu}{are}\mspace{14mu}{Eotvos}} \\{{{or}\mspace{14mu}{in}\mspace{14mu} 10^{- 9}\mspace{14mu}\sec^{- 2}},{{or}\mspace{14mu}{equivalent}}}\end{matrix}$

These devices should not be confused with gravimeters which measure thegravitational field, for instance by measuring the weight of a knownmass within the gravitational field.

There is interest in improving the performance of the GGI in an aircraftfor the purpose of detecting gravity disturbances caused by geologicaldensity anomalies associated with economic mineral or hydrocarbondeposits.

BACKGROUND ART

Measurements of gravity can be made from aircraft, and are routinelyused in some resource exploration, particularly petroleum exploration. Ameasurement of gravity gradient is preferred for detection of gravitydisturbances from an airborne platform, because the direct measurementof gravity cannot distinguish the gravity signal from accelerationsassociated with the motion of the aircraft. This effect is morepronounced at low altitude surveying, preferred in mineral explorationto improve spatial resolution of the survey, because of the prevalenceof atmospheric turbulence close to the ground surface. An ideal gravitygradient measurement will not be sensitive to the motion of themeasurement instrument.

A principal source of measurement noise (error) is residual sensitivityof the GGI to motion. The magnitude of the gravity gradient signalexpected from an economic mineral deposit is in the range of 1–100Eotvos (1 Eotvos=10⁻⁹ (m/s²)/m). Accelerations experienced in a surveyaircraft during low level surveys are generally of the order of 1 m/s²and the GGI has a baseline length of 10 cm. The acceleration rejectionof the GGI therefore must be of the order of one part in 10⁹. The GGIincorporates some mechanisms to achieve high rejection of accelerationbut further improvements are required to enable those mechanisms tooperate more effectively.

SUMMARY OF THE INVENTION

The invention is a gravity gradient instrument, comprising:

a first, second, third and fourth accelerometer equally spaced aroundthe circumference of a circle, with their sensitive axes tangential tothe circle, and arranged in opposing pairs with the first accelerometeropposite the second, and the third accelerometer opposite the fourth; inuse the accelerometers are spun around an axis normal to the circle andpassing through its centre;

a summing amplifier which receives the outputs of the accelerometers andcombines them in a manner to cancel the common mode output signals, toproduce an instrument output; and

one or more feedback loops extending from the instrument output to oneor more of the accelerometers to compensate for errors; the feedbackloops including one or more additional inputs over and above theinstrument output Those additional inputs including one or more of thefollowing, taken alone or in combination.

Signals measuring one, two or three components of the accelerationenvironment of the gravity gradient instrument. These signals may bederived from accelerometers used on the inertial platform on which thegravity gradient instrument is usually mounted.

Signals measuring one, two or three components of the accelerationenvironment of the gravity gradient instrument rotor. The signalsmeasuring the acceleration components in the plane of the gravitygradient instrument accelerometers may come from those accelerometers.

Signals measuring the attitude of the aircraft (roll, pitch andheading).

Signals measuring the rotational rates of the gravity gradientinstrument.

Signals measuring the physical environment of the gravity gradientinstrument.

Signals representing the flight conditions of the airborne instrument,such conditions including fuel levels on survey; in turn between surveylines; takeoff, climb/descend. These signals may be automaticallydetermined from flight instruments or may be manually entered by anoperator or pilot.

The enhanced feedback loops may be implemented as a part of the gravitygradient instrument and its support electronics. They may also beimplemented by means of an external processing unit connected to thegravity gradient instrument. This implementation has the benefit ofrequiring minimal change to the gravity gradient instrument itself.

The operation of prior art feedback loops may in some circumstances bedetrimental to the operation of the gravity gradient instrument. Theextent to which the operation of a feedback loop is beneficial ordetrimental to the operation of the gravity gradient instrument can bedetermined from the above identified additional inputs to the feedbackloops, and the gain or operation of the feedback loop adjustedappropriately.

The sensitivity of the gravity gradient instrument to an accelerationstimulus may be determined by correlating the instrument output with ameasurement of the stimulus. The feedback loop may then operate byapplying feedback to an accelerometer to remove that sensitivity on thebasis of the determined correlation.

The sensitivity of the gravity gradient instrument to its environment,as measured by the above identified additional inputs, may likewise bedetermined by a correlation process. Once determined this sensitivitymodel can be used to determine what contribution these sensitivitiesmake to the output of the gravity gradient instrument. Subtraction ofthis component from the instrument output as it is applied to thefeedback loop reduces the noise on this primary input to the feedbackloops and in turn further reduces the noise on the gravity gradientinstrument output.

BRIEF DESCRIPTION OF THE DRAWINGS

An example of the invention will now be described with reference to theaccompanying drawings, in which:

FIG. 1 is a gravity gradiometer instrument having four accelerometers.

FIG. 2 is a block diagram of known active feedback loops.

FIG. 3 is a block diagram of the active feedback loops used in theinvention.

FIGS. 4 to 10 are block diagrams illustrating various ways in which theactive feedback loops of the invention may be applied to the knownfeedback loops of FIG. 2.

BEST MODES OF THE INVENTION

Referring first to FIG. 1, the GGI consists of four, 1, 2, 3 and 4 (oreight) high quality, low noise, matched accelerometers mounted on ablock 5 as shown in FIG. 1. Each of the GGI accelerometers hasmechanisms for trim adjustment of: the accelerometer scale factor, andthe alignment of the accelerometer sensitive axis. The alignment trimadjustment is nominally about the accelerometer output axis.

The nominal configuration of the GGI accelerometers has theaccelerometers 1, 2, 3 and 4 equally spaced on the circumference of acircle, with their sensitive axes tangential to the circle. The block isrotated about an axis 6 (the spin axis) which is nominally and to a highprecision perpendicular to the plane of the circle, and passes throughthe centre of the circle. The rotation rate (Ω) is usually 0.25 Hz andcan vary from 0.25 Hz to 1.67 Hz.

The outputs of the four accelerometers are combined by a summingamplifier 7 as shown in FIG. 2. This combining of the outputs must bedone in a way which allows the large common mode accelerometer outputsignals to cancel to a high degree of precision, so that the residualdifferences which constitute the gradient signal are observable. In FIG.2 the outputs from accelerometers 3 and 4 are subtracted from theoutputs from accelerometers 1 and 2 to achieve common mode cancellation.

In the nominal configuration of the GGI and if the accelerometersensitivities are exactly equal, the GGI is not sensitive totranslational accelerations or to rotations about the spin axis. The GGIretains a sensitivity to the rate of rotation about axes in the plane ofthe circle (X and Y in FIG. 1), and this source of noise (error) isreduced by mounting the GGI in a high quality inertially stabilisedgimbals.

The GGI will have a residual sensitivity to translational motion whichis the result of, and proportional to, the difference in thesensitivities of each diametrically opposite pair of accelerometers.

The GGI of FIG. 2 incorporates active feedback control to continuouslymatch the sensitivities of the accelerometers in each pair called Scalefactor feedback. These feedback controls require there to be a distinctsignal in the GGI output which is the result of the mismatch ofsensitivity of a pair of accelerometers. Such a signal occurs when thespin axis is inclined from the vertical α (FIG. 1). This results in eachaccelerometer sensing the gravitational acceleration modulated by therotation of the GGI rotor. The resultant component of the GGI output isΔ₁₂ Kg sin (θ_(v)) sin (Ωt) for one pair and Δ₃₄ Kg sin (θ_(v)) cos (Ωt)for the other pair. The active feedback controls sense the magnitude ofthese signals by synchronous demodulation of the GGI output, and adjustthe sensitivity of one of the accelerometers of the corresponding pairto null the signal. θ_(v), is the angle by which the GGI spin axis istilted from the vertical.

The GGI will have a residual sensitivity to rotational accelerationsabout the spin axis whenever there is a mismatch in the meansensitivities of the two pairs of the accelerometers. The GGI alsoincorporates a feedback control to adjust this mismatch by adjusting thesensitivity of a third accelerometer. This is called spin modulation, orscale factor pair feedback. This loop relies on active modulation of theGGI spin rate at another frequency (typically 1.8 Hz) to provide thefeedback signal. The resultant component of the GGI output is(Σ₁₂K–Σ₃₄K)θ_(s)ω_(s) ² sin(ω_(s)t). The active feedback control sensesthe magnitude of this signal by demodulation of the GGI output, andadjusts the sensitivity of one of the accelerometers of the set of fourto null out the signal. θ_(s) is the angular amplitude of the spinmodulation.

The active feedback loops are shown schematically in FIG. 2. For eachloop the output of the GGI is demodulated by multiplication by asinusoidal signal at the frequency of the loop stimulus and in phasewith the residual response to that stimulus. The demodulated signal ispassed through a low pass filter including an integrator before beingfed back to the appropriate accelerometer control point.

Gravity Gradient Instruments operated with compensation loops asdescribed above do not always function as intended in airborneoperation. These loops function by detection of a signal component inthe output of the GGI which is dependent on an input stimulus. For theprimary compensations which correct for mis-match of accelerometersensitivity between pairs of accelerometers, this stimulus is thecomponent of the Earth gravity vector in the tilted plane of the GGIrotor. In airborne operation, for example when the aircraft executes aturn, there is a considerable additional acceleration term in thehorizontal plane, which adds as a vector sense to the Earth gravityvector.

As this additional acceleration is typically a considerable fraction ofthe Earth's gravity, the stimulus to this compensation loop is changedand the loop will function abnormally. In the case of a small tilt angleto the GGI, the action of the compensation loop can be reversed, so thatits effect is to drive the accelerometer scale factors apart, ratherthan making them equal. The effect of this is to make the GGI moresensitive to the acceleration environment of the aircraft, negating thebenefit from a gradiometric measurement.

Referring now to FIG. 3. The active feedback 30 of the invention usesone or more external signals 31 to alter the operation of the feedbackloop. This feedback loop may include as before a demodulation functionfollowed by a filter function. As shown in FIG. 4 the external signalmay be a signal indicating the aircraft is turning and this is used toalter the operation of the feedback loop during the turn. This signalcould be derived from the aircraft controls; the aircraft instruments;the pilot or operator; or from the acceleration environment of thegravity gradient instrument exceeding a threshold level of horizontalacceleration.

The demodulation function in the prior art feedback loops effects acorrelation of the output of the gravity gradient instrument withassumed acceleration environment of the accelerometer pair on which thefeedback operates, where the assumed acceleration environment is justthe stationary Earth gravity vector coupled with the tilt of the gravitygradient instrument. It is when this assumed acceleration environment iswrong in sign, that the compensation loop is detrimental to theoperation of the gravity gradient instrument.

Therefore another mode of operation of the feedback loop is to use acorrelation of the gravity gradient instrument output with the actualacceleration environment of the accelerometer pair. This involves, inthe place of the demodulation function, forming the product 50 of theinstrument output and the acceleration 32 measured by one accelerometerof the pair being compensated by the feedback loop and applying aconstant gain 51 related to the magnitude of the accelerationenvironment. This is shown in FIG. 5.

It is recognised that this scheme would allow the gravity gradientinstrument to operate without tilt in a dynamic situation and that thismay have further benefit to its performance.

It is recognised that the acceleration 32 can also be derived from othermeasures of the acceleration of the gravity gradient instrument.

The filter function is a low pass filter used to reduce high frequencynoise on the output of the compensation feedback as this contributes tothe noise on the output of the gravity gradient instrument. Thebandwidth of this filter is a trade-off between increased noise on theoutput of the gravity gradient instrument from noise on the feedback, asthe filter bandwidth is increased; and increased noise on the output ofthe gravity gradient instrument from reduced compensation of thesensitivity which the feedback is compensating, as the filter bandwidthis decreased. The amount of noise from the second of these effects isproportional to the amount of acceleration experienced by the gravitygradient instrument and when there is a higher acceleration level, it isdesirable to increase the gain of the feedback loop to better compensatethe sensitivity.

This can be achieved by (in parallel) forming the square 60 of theacceleration input; passing this through a low pass filter 61; and usingthe output of this filter, or a function of it, to determine the gain tobe applied in the feedback. As shown in FIG. 6.

The optimum gain to be applied in the feedback loop is also dependent onthe level of noise in the output of the gravity gradient instrument,particularly that component which is not a result of the sensitivitywhich the feedback loop is effecting, and on the characteristics of thevariation of the sensitivity which the feedback loop is tracking.Parameters (either static or determined dynamically) representing thesefactors 72, 73 may be combined with the instrument output and theacceleration 32 in a Kalman filter to generate the measure of themismatch of scale factors which is required to drive the feedback asshown in FIG. 7. The Kalman filter provides the optimum gain in linearsystems, however this feedback system is non-linear and it is notguaranteed that the result is optimum. An extended Kalman filter isapplicable to non-linear systems (S. M. Kay, Fundamentals of statisticalsignal processing: Estimation theory. Prentice Hall, 1993).

The Kalman filter 70 incorporates a model of the component of thegravity gradient instrument output which results from the sensitivity(scale factor mis-match) which the feedback loop is tracking. That modelis simply the product of the sensitivity (which is being estimated bythe Kalman filter) and the acceleration 32.

In all cases the noise on the output of the compensation feedback loopis derived from the noise on the output of the gravity gradientinstrument. Application of linear regression techniques to the gravitygradient instrument output shows that a large part of this noise isusually due to residual uncompensated sensitivity to the accelerationenvironment of the instrument and that it can be removed by theregression.

Further enhancement of the compensation loops can be obtained by removalof this deterministic noise from the output of the gravity gradientinstrument prior to, or as part of the feedback loop. The genericimplementation of this 90 is shown in FIG. 8.

The determination of the sensitivity function, f({umlaut over(x)},ÿ,{umlaut over (z)}) used in the scheme of FIG. 8 could be on thebasis of processing of previously acquired data, but it can also bedetermined during the processing in the feedback loops. The schemes ofFIGS. 4, 5, 6, and 7 are all suitable for estimation of some of theparameters needed for the scheme of FIG. 8. These and additionalparameters (Grierson, A. D., 1990, Gravity gradiometer survey systemstage I data reduction: Proc. of Seventeenth Annual Gravity GradiometerConf., GL-TR-90-0067, ADA223568, Geophysics Laboratory, Air ForceSystems Command, Hanscom Air Force Base provides a suitable model of thesensitivities) may also be estimated by a regression technique. Apreferred approach is to extend the Kalman filter of FIG. 7 toincorporate these sensitivities as part of its system model, as anextended vector Kalman filter.

It is further recognised that components of the gravity gradient outputwhich will act as noise in the compensation loops, are measured gravitygradients. These gradients include the self gradient of the surveysystem including the aircraft in which the system is mounted, which is afunction of the attitude of the aircraft; and the acceleration gradientsdue to rotation of the gravity gradient instrument are a function of therotation rates of the instrument.

These signals can therefore be subtracted from the output of the gravitygradient instrument as the first stage of the feedback compensations;see FIG. 9.

The system model incorporated in particular in the schemes describedusing a Kalman filter can be extended to include other known influencesof measurable parameters on the sensitivities of the gravity gradientinstrument As an example the gravity gradient instrument is known to bevery sensitive to temperature variation, thus a measure of thetemperature of the gravity gradient instrument can be used as aparameter in the model of the instrument output to further improve theperformance of the compensations.

It is further recognised that the least noise on the output of thegravity gradient instrument, from the feedback loops is obtained whenthe loops are not active. Therefore another mode of operation is tointerrupt output of the compensation loops using switch 111 at any timethat the instrument is gathering data (on survey), but allow processingby the feedback loops during this time, and then reconnect the output ofthe loop to the gravity gradient instrument accelerometer control pointwhen the instrument is not being used to gather data (for example duringturns at the end of survey lines) See FIG. 10.

The Figures show only one feedback. The schemes are applicable tomultiple parallel feedbacks. The schemes can be mixed and severalapplied to a single feedback, particularly FIG. 10 in association withany other scheme.

Physical Implementation

One mode of implementation of the invention is an external computationaldevice which receives data from the gravity gradient instrument, forexample as data being recorded to a file on the external device. Afurther communication link or an electrical interface allows theexternal device to communicate the output of its feedback compensationloops to the appropriate control points on the accelerometers of thegravity gradient instrument.

Another mode of implementation would implement the combination of thesignals required for these enhanced compensation feedbacks asmodifications of the feedback processing of the prior art compensations.

1. A gravity gradient instrument, comprising: a first, second, third andfourth accelerometer equally spaced around the circumference of acircle, with the accelerometer sensitive axes tangential to the circle,and arranged in opposing pairs with the first accelerometer opposite thesecond accelerometer and the third accelerometer opposite the fourthaccelerometer; in use the accelerometers are spun around an axis normalto the circle and passing through the circle's centre; a summingamplifier which receives outputs of the accelerometers and combines themin a manner to cancel common mode output signals, to produce aninstrument output; and one or more feedback loops extending from theinstrument output to one or more of the accelerometers to compensate forerrors; wherein the feedback loop or loops include one or moreadditional inputs in addition to the instrument output, the additionalinputs including signals representing one or more of: components ofattitude, velocity and acceleration, the physical environment and flightconditions, taken alone or in combination.
 2. A gravity gradientinstrument according to claim 1, wherein the additional inputs includesignals measuring one, two or three components of the accelerationenvironment of the gravity gradient instrument.
 3. A gravity gradientinstrument according to claim 2, wherein the gravity gradient instrumentis mounted on an internal platform and the signals are derived from theaccelerometers used on the inertial platform.
 4. A gravity gradientinstrument according to claim 1, wherein the additional inputs includesignals measuring one, two, or three components of accelerationsexperienced by the gravity gradient instrument.
 5. A gravity gradientinstrument according to claim 4, wherein the signals measuring thecomponents of acceleration in the plane of the gravity gradientinstrument accelerometers come from the gravity gradient accelerometers.6. A gravity gradient instrument according to claim 1, wherein theadditional inputs include signals measuring the attitude of an aircraft.7. A gravity gradient instrument according to claim 1, wherein theadditional inputs include signals measuring rotational rates of thegravity gradient instrument.
 8. A gravity gradient instrument accordingto claim 1, wherein the additional inputs include signals measuring thephysical environment of the gravity gradient.
 9. A gravity gradientinstrument according to claim 1, wherein the additional inputs includesignals representing the flight conditions of an airborne instrument.10. A gravity gradient instrument according to claim 9, where theconditions include fuel levels on survey.
 11. A gravity gradientinstrument according to claim 9, where the conditions include turnsbetween survey lines.
 12. A gravity gradient instrument according toclaim 9, where the conditions include take-off.
 13. A gravity gradientinstrument according to claim 9, where the conditions include climb ordescend.
 14. A gravity gradient instrument according to claim 9, wherethe signals are automatically determined from flight instruments.
 15. Agravity gradient instrument according to claim 1, wherein the feedbackloops are implemented as a part of the gravity gradient instrument andthe gravity gradient instruments support electronics.
 16. A gravitygradient instrument according to claim 1, wherein the feedback loops areimplemented by means of an external processing unit connected to thegradient instrument.
 17. A gravity gradient instrument according toclaim 1, wherein the additional inputs are used to determine theperformance of a feedback loop and the gain or operation of saidfeedback loop is then adjusted.
 18. A gravity gradient instrumentaccording to claim 1, wherein the sensitivity of the gravity gradientinstrument to an acceleration stimulus is determined by correlating theinstrument output with a measurement of the stimulus and then applyingfeedback to one of the first, second, third or fourth accelerometers toremove that sensitivity on the basis of the determined correlation. 19.A gravity gradient instrument according to claim 1, wherein thesensitivity of the gravity gradient instrument to errors, as measured byrespective additional inputs, is determined by a correlation process,then the contribution the sensitivity relating to each additional inputmakes to the output of the gravity gradient instrument is determined andthis contribution is subtracted from the instrument output as it isapplied to the feedback loop to reduce the noise of this primary inputto a respective feedback.